1. Field of the Invention
The invention pertains to a method for predicting propagation of sound in an ocean.
2. Description of the Related Art
For the purpose of predicting propagation of sound in an ocean, the ocean can be modelled as a three-dimensional acoustic waveguide that is spatially irregular. A partial differential wave equation governs propagation of sound in the waveguide. A complex-valued distribution of pressure represents the sound field in this equation. However, the sound field also can be represented in terms of the local modes of the waveguide. This representation is useful because it reduces the dimensionality of the model. The equations that govern this representation are obtained by taking moments of the wave equation with respect to the local modes. These moments produce a system of coupled mode equations in two horizontal dimensions. The solution of these coupled mode equations can be used to reconstruct the sound field at any depth in the waveguide from the local mode representation.
In FIG. 1 there is shown a circular region 10 in the horizontal plane with a source of sound at the center 12. An article by A. T. Abawi, W. A. Kuperman and M. D. Collins (“The coupled mode parabolic equation”, Journal of the Acoustical Society of America, Vol. 102, No. 1, pp. 233-238, July 1997) discusses a numerical method for solving coupled mode equations to predict propagation of sound over region 10. This method is an elaboration of an earlier numerical method that was developed by M. D. Collins ignoring coupling among the modes. Propagation of sound is predicted over all of region 10. The preferred direction of propagation is the radially outward direction from the center 12.
An article by M. D. Collins (“The adiabatic mode parabolic equation”, Journal of the Acoustical Society of America, Vol. 94, No. 4, pp. 2269-2278, October 1993) points out that it would be very efficient to make predictions just over an angular sector 14 of small angular width. The article notes that transparent boundary conditions would have to be imposed along the radial edges of sector 14 for this purpose, but it does not indicate how to formulate these conditions or how to adopt them in a solution method. The article by A. T. Abawi, W. A. Kuperman and M. D. Collins does not address these issues at all.